Plotting

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

%matplotlib inline

• Matplotlib is the most widely used plotting library in the ecosystem of python. In the above cel we loaded matplotlib and the relevant libraries.

• The easiest way to use matplotlib is via pyplot, which allows you to plot 1D and 2D data. Here is a simple example:

# Compute the x and y coordinates for points on a sine curve
x = np.arange(0, 3 * np.pi, 0.1)
y = np.sin(x)

# Plot the points using matplotlib
plt.plot(x, y)

[<matplotlib.lines.Line2D at 0x7f12b57e4350>]

if we want to customize plots it is better to plot by first defining fig and ax objecs which have manuy methods for customizing figure resolution and plot related aspects respecticely.

fig, ax = plt.subplots()

y_sin = np.sin(x)
y_cos = np.cos(x)

# Plot the points using matplotlib
ax.plot(x, y_sin)
ax.plot(x, y_cos)

# Specify labels
ax.set_xlabel('x axis label')
ax.set_ylabel('y axis label')
ax.set_title('Sine and Cosine')
ax.legend(['Sine', 'Cosine'])

#fig.savefig("myfig.pdf")

<matplotlib.legend.Legend at 0x7f12b56e8850>

A gallery of useful examples

For a greater variety of plotting examples check out Matploltib Gallery!

1D plotting is conveniently done by creating fig and ax objects which allow coutom styling plots and figure properties separately.

fig, ax = plt.subplots()          # Create fig and ax objects

t = np.arange(0.0,  2*np.pi, 0.1) # create x values via np.arange or np.linspace

s = np.sin(t)                     # create y values

ax.plot(t, s, '-o')                     # make the plot

#fig.savefig('myFIG.png')         # save figure

[<matplotlib.lines.Line2D at 0x7f12b40c53d0>]

fig and ax objects

For customizing plots it is more convenient to define fig and ax objects. One can then use ax object to make veriety of subplots then use fig to save the entire figure as one pdf. Try changing fig size, number of columns and rows.

t = np.arange(0.0,  2*np.pi, 0.1) # create x values
s = np.sin(t)                     # create y values

fig, ax = plt.subplots(nrows=1,ncols=2,figsize=(6,3))          

ax[0].plot(t, s,'-o', color='purple', lw=1.0)  # plot on subplot-1
ax[1].plot(t, s**2,'-o', color='green',  lw=1.0)  # plot  on subplot-2

#fig.savefig('sd.png')             # save the figure

[<matplotlib.lines.Line2D at 0x7f12affdd950>]

Plotting in 2D

To make 2D plots we need to generate 2D grid \((x,y)\) of points and pass it to our function \(f(x,y)\)

\[f(x,y) = sin(x) \cdot cos(x) \,\,\,\]

x = np.arange(0.0,  2*np.pi, 0.1)   # create x values
y = np.arange(0.0,  2*np.pi, 0.1)   # create y values

X, Y = np.meshgrid(x,y)             # tunring 1D array into 2D grids of x and y values

Z = np.sin(X) * np.cos(Y)           # feed 2D grids to our 2D function f(x,y)

fig, ax = plt.subplots()            # Create fig and ax objects
ax.pcolor(X, Y, Z,cmap='RdBu')                  # plot 

# try also ax.contour, ax.contourf

<matplotlib.collections.PolyCollection at 0x7f12d865f790>

3D plots with matplotlib

from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D

# Create fig and ax objects for 3d plotting
fig = plt.figure()
ax = fig.add_subplot(projection='3d')  

# Using X,Y,Z grid of points in previous step 
C = ax.plot_surface(X, Y, Z, cmap='RdYlBu')

# Set distance and angle view
ax.view_init(30, -140)
ax.dist = 9

# Add a colorbar
fig.colorbar(C, ax=ax, 
             label='$Z(X,Y)$', 
             shrink=0.4, 
             aspect=10) 

<matplotlib.colorbar.Colorbar at 0x7f12b57af150>

Plotting histograms with matplotlib

# Make up some random data
mu, sigma = 100, 15
x = mu + sigma * np.random.randn(10000)

# Plot 1D histogram of the data
plt.hist(x, bins=40, density=True);

# Make up some random data
mu, sigma = 100, 15
x = mu + sigma * np.random.randn(10000)
y = mu + 2*sigma * np.random.randn(10000)

# Plot 2D histogram of the data
plt.hist2d(x, y, bins=40, density=True, cmap='RdBu_r');

Statistical visualizations with seaborn

• Seaborn For visualizing statistical plots there is a specialized library build on top of matplotlib that simplifies many intermediate steps that are needed to go from data to beautiful and polished visualization.

import seaborn as sns

# Make up some random data
data= 10+2*np.random.randn(10000)

sns.displot(data, kind="kde")

<seaborn.axisgrid.FacetGrid at 0x7f12a9862fd0>

Seaborn works great with dataframes

# loading dataset https://github.com/mwaskom/seaborn-data

data = sns.load_dataset("car_crashes")

data.head()

	total	speeding	alcohol	not_distracted	no_previous	ins_premium	ins_losses	abbrev
0	18.8	7.332	5.640	18.048	15.040	784.55	145.08	AL
1	18.1	7.421	4.525	16.290	17.014	1053.48	133.93	AK
2	18.6	6.510	5.208	15.624	17.856	899.47	110.35	AZ
3	22.4	4.032	5.824	21.056	21.280	827.34	142.39	AR
4	12.0	4.200	3.360	10.920	10.680	878.41	165.63	CA

sns.jointplot(data = data, 
              x = "speeding", 
              y = "alcohol", 
              kind = "kde"
              )

<seaborn.axisgrid.JointGrid at 0x7f12a9179350>

Interactive plots

Plotly

• Plotly is large multi-language interactive graphing library that covers Python/Julia/R.

• Plotly-dash is a framework for building web dashborads with itneractive plotly graphs.

• Plotly-express is a high level library for quick visualizations whihc is similiar to seaborn vs matploltib in its philosophy

Check out this cool website built using Dash-Plotly

import plotly.express as px

df = pd.DataFrame({ 'X':    1*np.random.randn(500), 
                    'Y':    5*np.random.randn(500), 
                    'Z':    1+5*np.random.randn(500),
                    'time':  np.arange(500)
                  })

px.density_heatmap(df, x='X', y='Y')
#px.line(df, x='X', y='Y')
#px.scatter(df, x='X', y='Y')
#px.area(df, x='X', y='Y')
#px.histogram(df, x="X")

fig = px.scatter(df, x="X", y="Y", size=20*np.ones(len(df)), 
                 animation_frame="time", animation_group='Y', color='Y',
                 range_x=[-20,20], range_y=[-20,20]
                 )
fig.show()

Holoviews

Stop plotting your data - annotate your data and let it visualize itself

• There are too many options for visualizing data and it is impossible to settle on one because different libraries have different strengths depending on the nature of data and visualization.

• One emerging idea in scientific software design is to create library agnostic tools. E.g if you want to plot histogram you can do it either using several different libraries or using a library agnostic tool by specifying the particular library interface for the visualization.

• Holoviews provides interface for using matplotlib, plotly, bokeh plotting through a single high level interface.

import holoviews as hv

hv.extension('matplotlib')  # try 'plotly' or 'matplotlib'

data = np.random.randn(20)

# multiplying creates overlay, adding crates subplots
hv.Curve(data) * hv.Scatter(data) + hv.Curve(data)

hv.extension('plotly')

Z = np.sin( np.random.randn(40,40) )
hv.Surface(Z, bounds=(-5, -5, 5, 5))

Widgets

Suppose we would like to explore how the variation of parameter \(\lambda\) affects the following function of a standing wave:

\[f(x) = sin (\omega \cdot x +p)\]

• Make a python-function which creates a plot as a function of a parameter(s) of interest.

• Add an interactive widget on top to vary the parameter.

from ipywidgets import widgets

# in jupyter notebook may need to add %matplotlib inline to top cell

@widgets.interact(phase=(0,2*np.pi), freq = (0.1,5))  
def wave(phase=0, freq=0.5):          
    
    x  = np.linspace(0,10,1000)
    y  = np.sin(freq*x+phase)
        
    plt.plot(x, y)

Holoviews and Dynamic Map

In addition to jupyter widgets Holoviews provides alternative way of creating widgets for data exploration.

hv.extension('plotly')

def wave(phase, freq):
    
    x  = np.linspace(0,10,100)
    y  = np.sin(freq*x+phase)
    
    return hv.Curve( (x,y) )

# Create dynamic map
dmap = hv.DynamicMap(wave, kdims=['phase', 'freq'])

# Specify variables and ranges
dmap.redim.range(phase=(0.0,2*np.pi), freq=(0.1, 5))             

def rand_image(idx):
    '''Generate a sequence of 2D images with normally distributed numbers
    time = length of trajectory or num of images
    '''
    
    data = np.random.randn(1000, 50, 50)
    
    return hv.Image( data[idx] )

# create dynamic map
dmap = hv.DynamicMap(rand_image, kdims=['time'])

# Specify variables and ranges
dmap.redim.range(time=(1,10))  

Additional resoruces.

Matplotlib has a huge scientific user base. This means that you can always find a good working template of any kind of visualization which you want to make. With basic understanding of matplotlib and some solid googling skills you can go very far. Here are some additional resources that you may find helpful

• Matplotlib

• Matplotlib Book

• Matplotlib Blog

• PyViz universe

• The Python Graph Gallery